Nonextensive Statistical Mechanics

174 5 Deterministic Dynamical Foundations of Nonextensive Statistical MechanicsTTBG ≡1/12 ã = 100.080.060.040.020ã = 0.6ã = 0.4 ã = 0.35ã = 0.3ã = 0.2t 210 0 10 1 10 2 10 3 10 4 10 5 tt 3(a)1/t c(b)0.10.0500 0.2 0.4 5.2ã(c)4d ã = 0.4fã = 0.33.5 ã = 0.25ã = 0.232.5210 0 10 1 10 2 10 3 10 4 10t5Fig. 5.23 (a) Time evolution of the dynamical temperature T of two coupled standard maps, forb = 2 and typical values of ã. We start with water bag initial conditions (M = 1296 points with0 ≤ θ 1 ,θ 2 ≤ 1, and p 1 , p 2 = 0.25±5·10 −3 ); moreover, an average was taken over 35 realizations.See Fig. 5.22 for t 2 and t 3 .(b) Inverse crossover time t c vs. 1/ã 5.2 .(c) Time evolution of the fractaldimension of a single initial ensemble in the same setup of (a) (from [356]).T0.20.150.1ã = 0.4ã = 0.6ã = 10T BG≡1/12ã = 0.1ã = 0.2ã = 0.3ã = 0.3510 0 10 1 10 2 10 3 10 4 10 5 t1/t c0.20.100 0.25 0.5ã0.9Fig. 5.24 Same as Fig. 5.23(a),(b) but with “double water bag” initial conditions: 0 ≤ θ 1 ,θ 2 ≤ 1;p 1 , p 2 randomly distributed inside one of the two regions p 1 , p 2 = 0 + 10 −2 , p 1 , p 2 = 1 − 10 −2(from [356]).